Problem: Solve for $x$: $$ \frac{1}{2} - \frac{1}{3} = \frac{1}{x}.$$
Explanation: Subtract 1/3 from 1/2 by finding a common denominator: \[
\frac{1}{2}-\frac{1}{3}=\frac{3}{6}-\frac{2}{6}=\frac{1}{6}.
\] Solving $\frac{1}{6}=\frac{1}{x}$ we find $x=\boxed{6}$.